There are some "easy" to care for plants on sale (buy one get one free) at my local pet store. I wanted to ask if anyone here has them and if they are indeed something I could handle as a newbie to aquarium plants.

They are:

Bacopa (Bacopa caroliniana)

Dwarf Sagittaria (Sagittaria subulata, dwarf)

Apparently both can be planted in aquarium gravel and the light I will have should be sufficient for both. I'm getting a 5 gallon tank, in case that matters. One of them needs iron "in the substrate". Now, the liquid plant food I got has "Pot. ash" and iron in it already. Will I need some other type of plant food?

Two very nice plants-a stem type (Bacopa caroliniana) and a rosette type (Sagittaria subulata, dwarf)-both will do well in moderate light and should do well in your 5g tank

The stem is easy to propagate by pinching the top and re-planting and the rosette will send out runners

When you plant the sag make sure and keep the crown above the substrate-I like to give it a little tug to pull it upward after I plant the roots-its better to plant too shallow than too deep so the crown doesn't rot
On the stem plant it doesn't matter- but try to keep them far enough apart so the light can reach the lower leaves and pinch the leaves off the lower stem so they are not in the substrate/gravel.

I don't feed mine- I have soil based tanks so I don't need to-however-the Seachem line of plant products has a good reputation.

I have another question now. Can I use soil instead of gravel? There is a river in my back yard (I rent this place) and I could get some river bottom mud. Would that not make for a messy tank? Or, at least make it nearly impossible to do a 100% water change? Maybe for a beginner I should just stick with gravel..?

I would not use the river mud-I did this once and what a mess-the silts would never settle.....

In the natural planted tanks you need lots and lots of stem plants to start-about 75-80% of the floor planted and some floating plants.

I would stick to the gravel for now and do some research on the Walstad natural planted tanks and learn more about plant needs-every tank is different and what plant grows well for one may not for another and it can vary from tank to tank as well.

With rooted plants you don't want to make 100% water changes and disrupt the roots-it is not needed either-your stem plants when actively growing will function as a filter of sorts and use the ammonia produced by the fish as plant food....... thats the beauty of live active growing stem plants.

Bacopa is easy, a very fast grower with low light demands. :) My dwarf sags ended up dying, meh--I think it's because I had them right under my t5HO lights, so they stunted and eventually I got annoyed and moved them and they never recovered. My favorite plants are stem plants like bacopa and rotala rotundifolia, they're very forgiving, grow in a range of different light, and with one small batch of cuttings you can eventually fill a whole tank from simply pruning it and replanting the new cuttings.

Since you're a beginner with plants, I wouldn't go the soil route--you can use regular inert gravel with root tabs or you can use an enriched gravel made for planting in like Flourite or EcoComplete (what I use). Very easy to clean, and if you like to move your plants around, or have bottom dwellers or fish that like to dig around, then you don't have to worry about the substrate being agitated and clouding the water.